A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm.
At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured
with U = 0 at x = 0) is U = 3 J. When it is at x = xm, the kinetic and potential energies are:

A.

K = 5 J and U = 3 J

B.

K = 5 J and U = −3 J

C.

K = 8 J and U = 0

D.

K = 0 and U = 8 J

E.

K = 0 and U = −8 J

2.

For a completely inelastic two-body collision the kinetic energy retained by the objects is the
same as:

A.

the total kinetic energy before the collision

B.

the diﬀerence in the kinetic energies of the objects before the collision

C.

1
2
Mv
2
com, where M is the total mass and vcom is the velocity of the center of mass

D.

the kinetic energy of the more massive body before the collision

E.

the kinetic energy of the less massive body before the collision

3.

A certain spring elongates 9.0 mm when it is suspended vertically and a block of mass M is
hung on it. The natural angular frequency of this block-spring system:

A.

is 0.088 rad/s

B.

is 33 rad/s

C.

is 200 rad/s

D.

is 1140 rad/s

E.

cannot be computed unless the value of M is given

4.

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the
system has an energy of 6.0 J, then the maximum speed of the block is:

A.

0.06 m/s

B.

0.17 m/s

C.

0.24 m/s

D.

4.9 m/s

E.

6.9 m/s

5.

At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass each other without colliding. At the end of 2.0 s the
height above Earth’s surface of the center of mass of the two-ball system is:

A.

2.9 m

B.

4.0 m

C.

5.0 m

D.

7.1 m

E.

10.4 m

6.

Whenever an object strikes a stationary object of equal mass:

A.

the two objects cannot stick together

B.

the collision must be elastic

C.

the ﬁrst object must stop

D.

momentum is not necessarily conserved

E.

none of the above

7.

It is impossible for two particles, each executing simple harmonic motion, to remain in phase
with each other if they have diﬀerent:

A.

masses

B.

periods

C.

amplitudes

D.

spring constants

E.

kinetic energies

8.

A student’s life was saved in an automobile accident because an airbag expanded in front of
his head. If the car had not been equipped with an airbag, the windshield would have stopped
the motion of his head in a much shorter time. Compared to the windshield, the airbag:

A.

causes a much smaller change in momentum

B.

exerts a much smaller impulse

C.

causes a much smaller change in kinetic energy

D.

exerts a much smaller force

E.

does much more work

9.

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves,
sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of
the cart is:

A.

constant and in the forward direction

B.

constant and in the backward direction

C.

variable and in the forward direction

D.

variable and in the backward direction

E.

zero

10.

The thrust of a rocket is:

A.

a gravitational force acting on the rocket

B.

the force of the exiting fuel gases on the rocket

C.

any force that is external to the rocket-fuel system

D.

a force that arises from the reduction in mass of the rocket-fuel system

E.

none of the above

11.

In simple harmonic motion, the magnitude of the acceleration is:

A.

constant

B.

proportional to the displacement

C.

inversely proportional to the displacement

D.

greatest when the velocity is greatest

E.

never greater than g

12.

A meter stick is pivoted at a point a distance a from its center and swings as a physical
pendulum. Of the following values for a, which results in the shortest period of oscillation?

A.

a = 0.1 m

B.

a = 0.2 m

C.

a = 0.3 m

D.

a = 0.4 m

E.

a = 0.5 m

13.

A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20 m apart, on
frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move:

A.

1.0 m

B.

3.3 m

C.

10 m

D.

12 m

E.

17 m

14.

In simple harmonic motion, the magnitude of the acceleration is greatest when:

A.

the displacement is zero

B.

the displacement is maximum

C.

the speed is maximum

D.

the force is zero

E.

the speed is between zero and its maximum

15.

A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a
4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless
surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the
right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with
a speed of 0.30 m/s. Since the only forces on the blocks are the force of gravity, the normal
force of the surface, and the force of the spring, we conclude that:

A.

the spring is compressed at the time of the observation

B.

the spring is not compressed at the time of observation

C.

the motion was started with the masses at rest

D.

the motion was started with at least one of the masses moving

E.

the motion was started by compressing the spring

16.

Which one of the following statements is true?

A.

the center of mass of an object must lie within the object

B.

all the mass of an object is actually concentrated at its center of mass

C.

the center of mass of an object cannot move if there is zero net force on the object

D.

the center of mass of a cylinder must lie on its axis

E.

none of the above

17.

A 10-kg block of ice is at rest on a frictionless horizontal surface. A 1.0-N force is applied in
an easterly direction for 1.0 s. During this time interval, the block:

A.

acquires a speed of 1 m/s

B.

moves 10 cm

C.

acquires a momentum of 1.0 kg · m/s

D.

acquires a kinetic energy of 0.1 J

E.

none of the above

18.

Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is
compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the
spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:

A.

20 J

B.

8 J

C.

310 J

D.

125 J

E.

50 J

19.

A block moves at 5.0 m/s in the positive x direction and hits an identical block, initially at
rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does
not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks
move along the x axis and the incident block has a speed in of:

A.

1.8 m/s

B.

5.0 m/s

C.

6.8 m/s

D.

7.1 m/s

E.

11.8 m/s

20.

For an oscillator subjected to a damping force proportional to its velocity:

A.

the displacement is a sinusoidal function of time.

B.

the velocity is a sinusoidal function of time.

C.

the frequency is a decreasing function of time

D.

the mechanical energy is constant.

E.

none of the above is true.

21.

At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of
the center of mass of the two-ball system is:

A.

11 m/s, down

B.

11 m/s, up

C.

15 m/s, down

D.

15 m/s, up

E.

20 m/s, down

22.

A block on a spring is subjected to a damping force that is proportional to its velocity and to
an applied sinusoidal force. The energy dissipated by damping is supplied by:

A.

the potential energy of the spring

B.

the kinetic energy of the mass

C.

gravity

D.

friction

E.

the applied force

23.

In simple harmonic motion, the restoring force must be proportional to the:

A.

amplitude

B.

frequency

C.

velocity

D.

displacement

E.

displacement squared

24.

Force:

A.

equals the negative integral (with respect to distance) of the potential energy function

B.

is the ability to do work

C.

is the rate of change of doing work

D.

equals the time rate of change of momentum

E.

has dimensions of momentum multiplied by time

25.

A particle moves back and forth along the x axis from x = −xm to x = +xm, in simple
harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:

A.

it is at x = 0 and is traveling toward x = +xm

B.

it is at x = 0 and is traveling toward x = −xm

C.

it is at x = +xm and is at rest

D.

it is between x = 0 and x = +xm and is traveling toward x = −xm

E.

it is between x = 0 and x = −xm and is traveling toward x = −xm

26.

A 3.00-g bullet traveling horizontally at 400 m/s hits a 3.00-kg wooden block, which is initially
at rest on a smooth horizontal table. The bullet buries itself in the block without passing
through. The speed of the block after the collision is:

A.

1.33 m/s

B.

0.40 m/s

C.

12.0 m/s

D.

40.0 m/s

E.

160 m/s

27.

Three physical pendulums, with masses m1, m2 = 2m1, and m3 = 3m1, have the same shape
and size and are suspended at the same point. Rank them according to their periods, from
shortest to longest.

A.

1, 2, 3

B.

3, 2, 1

C.

2, 3, 1

D.

2, 1, 3

E.

All the same

28.

Five particles undergo damped harmonic motion. Values for the spring constant k, the damping
constant b, and the mass m are given below. Which leads to the smallest rate of loss of
mechanical energy?

A.

k = 100 N/m, m = 50 g, b = 8 g/s

B.

k = 150 N/m, m = 50 g, b = 5 g/s

C.

k = 150 N/m, m = 10 g, b = 8 g/s

D.

k = 200 N/m, m = 8 g, b = 6 g/s

E.

k = 100 N/m, m = 2 g, b = 4 g/s

29.

The center of mass of a uniform disk of radius R is located:

A.

on the rim

B.

a distance R/2 from the center

C.

a distance R/3 from the center

D.

a distance 2R/3 from the center

E.

at the center

30.

Block A, with a mass of 4 kg, is moving with a speed of 2.0 m/s while block B, with a mass of
8 kg, is moving in the opposite direction with a speed of 3 m/s. The center of mass of the two
block-system is moving with a velocity of:

A.

1.3 m/s in the same direction as A

B.

1.3 m/s in the same direction as B

C.

2.7 m/s in the same direction as A

D.

1.0 m/s in the same direction as B

E.

5.0 m/s in the same direction as A

31.

A particle moves in simple harmonic motion according to x = 2 cos(50t), where x is in meters
and t is in seconds. Its maximum velocity in m/s is:

A.

100 sin(50t)

B.

100 cos(50t)

C.

100

D.

200

E.

none of these

32.

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium
point. Of the following times, at which time is it furthest from the equilibrium point?

A.

0.5T

B.

0.7T

C.

T

D.

1.4T

E.

1.5T

33.

A 0.20-kg object attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:

A.

0.0020 m

B.

0.10 m

C.

0.20 m

D.

25 m

E.

250 m

34.

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude
of the oscillation is limited by:

A.

the damping force

B.

the initial amplitude

C.

the initial velocity

D.

the force of gravity

E.

none of the above

35.

The physical quantity “impulse” has the same dimensions as that of:

A.

force

B.

power

C.

energy

D.

momentum

E.

work

36.

If the total momentum of a system is changing:

A.

particles of the system must be exerting forces on each other

B.

the system must be under the inﬂuence of gravity

C.

the center of mass must have constant velocity

D.

a net external force must be acting on the system

E.

none of the above

37.

At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a
mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15 m/s.
They move along nearby lines and pass without colliding. At the end of 2.0 s the magnitude of
the acceleration of the center of mass of the two-ball system is:

A.

0.25g

B.

0.50g

C.

0.75g

D.

g

E.

g/0.75

38.

An object attached to one end of a spring makes 20 complete oscillations in 10 s. Its period is:

A.

2 Hz

B.

10 s

C.

0.5 Hz

D.

2 s

E.

0.50 s

39.

Bullets from two revolvers are ﬁred with the same velocity. The bullet from gun #1 is twice as
heavy as the bullet from gun #2. Gun #1 weighs three times as much as gun #2. The ratio
of the momentum imparted to gun #1 to that imparted to gun #2 is:

A.

2:3

B.

3:2

C.

2:1

D.

3:1

E.

6:1

40.

When you step on the accelerator to increase the speed of your car, the force that accelerates
the car is:

A.

the force of your foot on the accelerator

B.

the force of friction of the road on the tires

C.

the force of the engine on the drive shaft

D.

the normal force of the road on the tires

E.

none of the above

41.

An object on the end of a spring is set into oscillation by giving it an initial velocity while it
is at its equilibrium position. In the ﬁrst trial the initial velocity is v0 and in the second it is
4v0. In the second trial:

A.

the amplitude is half as great and the maximum acceleration is twice as great

B.

the amplitude is twice as great and the maximum acceleration is half as great

C.

both the amplitude and the maximum acceleration are twice as great

D.

both the amplitude and the maximum acceleration are four times as great

E.

the amplitude is four times as great and the maximum acceleration is twice as great